Is the word rir the same in Brazilian and European Portuguese?

No.

While the spelling, meaning, and the identity of the infinitive "rir" are identical in both dialects, there is a difference in typical usage and grammar regarding how the verb is used to express ongoing actions. In Brazil, the standard way to express the continuous aspect is through the gerund (rindo), whereas in Portugal, the construction a + infinitive (a rir) is used. Additionally, there are differences in pronunciation, specifically in the articulation of the "r" sound and the tendency to reduce or "swallow" vowels in many Brazilian dialects.

Brazilian Portuguese

1. Eu estava rindo muito ontem. (I was laughing a lot yesterday.)
2. Ela vive rindo de tudo o que eu digo. (She is always laughing at everything I say.)
3. A gente começou a rir do nada. (We started laughing out of nowhere.)
4. Pare de rir, por favor! (Stop laughing, please!)
5. Ele ri de nervoso quando fica ansioso. (He laughs nervously when he gets anxious.)

Continental Portuguese

1. Eu estava a rir muito ontem. (I was laughing a lot yesterday.)
2. Ela vive a rir de tudo o que eu digo. (She is always laughing at everything I say.)
3. Nós começámos a rir do nada. (We started laughing out of nowhere.)
4. Para de rir, por favor! (Stop laughing, please!)
5. Ele ri de nervoso quando fica ansioso. (He laughs nervously when he gets anxious.)